Saving paper!

Simply, we note that the number of characters in the essay is

$20 \ sheets * 55 \frac{lines}{sheet}* 65 \frac{characters}{line} = 71500 \ characters$

Now, after reformatting we have

$71500 \ characters * \frac{1 \ line}{70 \ characters} * \frac{1 \ page}{65 \ lines} = 15.71 \ characters \approx \boxed{20}$

FIRST YOU HAVE TO FIND TOTAL NUMBER OF WORDS IN FIRST CONDITION I.E. 20 SHEETS * 55 LINES * 65 WORDS= 71500 WORDS

NOW THIS IS ALSO THE NUMBER OF WORDS IN SECOND CONDITION NOW THE NUMBER OF SHEETS IN SECOND CONDITION IS 71500 WORDS / 70 WORDS /65 LINES= 15.714286

NOW BECAUSE THE OF SHEETS IS 15.714286 IT MEANS 1 MORE SHEET WILL BE USED AFTER 15 SHEETS I.E. 15.714286 MUST BE CONSIDERED AS 16 SHEETS

NOW THE PERCENTAGE REDUCTION IS

(20-16)/20*100 =20

EASEY PEASEY :)

reduction in pages = 20 - {(20x65)/70} which equals to 4.2857, and percent reduction = 4.2857x100/20 and the answer 21.4286 %

-first case:Total no of chars=20x55x65;

2nd case: total no of chars=sheetsx65x70;

characters will be same in both the case;

20x55x65=sheetsx65x70;

sheets=integer(15.7)=16;

16 is 80% of 20 sheets;

20% sheets are saved;

Book 1

55 lines x 65 characters = 3575 characters per page. So, For 20 pages, 3575x20= 71500 characters

Book 2

65 lines x 70 characters = 4550 characters per page. So, for 'x' pages, 4550 x 'x'=71500 characters So, No. of pages=71500/4550= 15.71 pages

Reduction Percentage= ((20-15.71)x100)/20

21.45%  ≈ 20%

Find the total number of characters and then divide by 65 x 70. The answer will be 11/14. So the reduction in pages will 3/14. Therefore, 3/14 x 100 % = 21.4 which is closest to 20.

Here first given that 20 pages 55lines 65char=71500char and N-pages 65lines 70char=71500char then N-pages=71500char (1/65lines) (1/70char)=15.714 ~=20

Because the question is not asking exact number of paper saved, so we just have to make a simple calculation of percentage for this problem.

% paper reduction = (1 - 55/65 x 65/70) x 100% = (1- 55/70 )x 100% = 21.42 % (approx 20%)

she 20 pages of 55 lines of 65 characters. so the total number of characters would be 20 55 65 which is equal to 71500 characters. let the number of new pages used be x. it consists of 65 lines which can contain 70 characters. so the eq becomes

x 65 70=71500 (as we know the total number of characters)

x=71500/4550=15.714. so she used 16 pages. now we have to find the reduction of pages.

using proportion: 100:20::x:16

100*16=20x

x=1600/20=80%

and so the reduction percentage would be 20%

Page reduction percentage same as character reduction percentage.

• Before, 55*65 = 3575 characters per page.
• Now, 70*60 = 4550 characters per page.

Converting to percentage, that's ~80%. 100-80 = ~20% Reduction.

no of characters she wrote = 65 55 20=71500 no of sheets that has 65 lines = 71500/(65*70)= 15.714 app.=20

number of characters = 20 55 65=71500 character number of largest sheets = 71500 / (65*70) = 15.714 approximetly = 20 (the answer)

The easiest way to calculate this rather than brute force is to realize that the proportion is the same as the reduction. Thus the proportion of NEW PAGES to OLD PAGES has the 20, and the 65's cancel out. You are left with 55 pages to 70 pages which is about 80%. Reverse that for a 20% reduction

(55 65/65 70)*100=78.5714 100-78.5714=21.4

In first case, let x be the total number of characters then x = 20 * 55 * 65 => 20 = x / 55 * 65 --------------equation(1)

In second case let no of pages be y but the number of characters in the essay will be same i.e. x then x = y * 65 * 70 => y = x / 65 * 70 ---------equation(2)

equation(2) / equation(1) y / 20 = (x / 65 * 70) / (x / 55 * 65) y / 20 = 55 / 70 y = 110 / 7 then % decrease in pages = {[20 - (110 / 7)] / 20} * 100 = 21.4 % = 20%(approx).

In one page of 55 lines and 65 characters are used that is 3575 in each page completed in 20 no of pages. thus total 71500. with 65 lines and 70 characterrs that is 4550 will be covering 71500 in 15.7 ( almost 16 pages) Now, she saves 20-16 =4 pages out of 20 that is 4/20 X100 =20 % Ans.

K.K.GARG,INDIA

$20 \times 55 \times 65 = x \times 65 \times 70$ $x = 15,7 ~ 16$ $\frac{16}{20} \times 100 percent = 80 percent$ $100 percent - 80 percent = \boxed{20 percent}$

This is how I did it:

20 sheets x 55 lines x 65 characters= 71500

20 sheets x 65 lines x 70 characters= 91000

91000-71500=19500

19500/100000=19.5/100 which is roughly equivalent to 20%

first calculate the number of pages in case of 65 lines and 70 characters.... then u'll easily calculate reduction percentage;)

Increase in lines by a factor of 65/55 = 13/11. Increase in characters per line by a factor of 70/65 = 14/13. Their product is 14/11, so the number of pages decreases by a factor of 11/14 which leaves about 80% of the original number of pages, a 20% reduction.

55 65 20 = 70 65 x (where x is number of pages used) x=15.71, now reduction in page = 4.29 and % of reduction is 21.45% and here nearest answer given is 20% so answer is 20%!

Number of sheets used in environment friendly way:206555=x6570=>x=16 Finally reduction percentage: (20-16)/20*100=20

She saved 3 and a half pages out of 20 pages. That is 18 % which is approximately 20%